An observation balloon floats over the Enemy lines and
the defenders decide to shoot it down. The defending gunners determine the balloon
is 3015 m above the ground at a distance of 5000 m. They fire a cannon at an angle of 40° with respect to
the horizon with an initial velocity of 760 m/s.

Solution

Place the origin at the bottom of the
anti-balloon gun. Define horizontal as the x-dimension with negative to the
left and vertical as the y-dimension with negative downward.

x-dimension

Start by finding time

in the x-dimension

vox = vo cos q

= (760
m/s) cos 40°

= 585
m/s

x = 1/2axt2 + voxt

= 0 + voxt

Solving for time gives:

t = x / vox

= (5000 m) / (585
m/s)

t = 8.55 sec

Finish in y-dimension >>>

y- dimension

voy = vo sin q

= (760
m/s) sin 40°

= 488
m/s

y = 1/2ayt2 + voyt

= 1/2 (-9.8 m/s2)(8.55 sec)2
+ 488 m/s)(8.55 sec)

y = 3814 m

While the actual height is 3815 m the cannon shell
will destroy the balloon if the fuse is set so that it explodes 3814 m
off the ground.

Conclusion and Significance

Typically the gun crew would be able to measure the range and height, but
they would have to calculate the angle. Air resistance and wind would
complicate the situation.

Insultingly Stupid Movie Physics is one
of the most humorous, entertaining, and readable physics books
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explanations for high school, 1st semester college
physics students, and film buffs.

It explains all 3 of Newton's laws, the 1st and
2nd laws of thermodynamics, momentum, energy, gravity, circular motion
and a host of other topics all through the lens of Hollywood movies
using Star Trek and numerous other films.

If you want to learn how to think physics and have a lot of fun in
the process, this is the book for you!